This book presents data-driven algorithms used in the context of wind farm modelling and exploits their relation with concepts from non-linear dynamical system theory. The algortihms include Input Output Dynamic Mode Decomposition and their combination with the Koopman Operator theory. The latter improves on modelling and analysis of the aerodynamic interaction between wind turbines in wind farms and assists in uncovering insights into the existing dynamics and improves models accuracy. The authors introduce the topic of wind farm flow control, illustrating current strategies devised to overcome power losses in wind plants due to the aerodynamic interaction between turbines. Although controlling wind farms as a whole is becoming increasingly important, the high dimensions and governing non-linear dynamics inherent of wind farm systems make the design of numerical optimal controllers computationally expensive. This book describes a possible pathway to circumvent this challenge through reduced order models that can embed the existing non-linearities. The authors make use of high fidelity open-source simulation datasets and developed algorithms to fully show the potential of this approach using visual results. The reader is motivated to use the datasets and algorithms and exploit the potential of the reduced order models.

The high dimensions and governing non-linear dynamics in wind farm systems make the design of numerical optimal controllers computationally expensive. A possible pathway to circumvent this challenge lies in finding reduced order models which can accurately embed the existing non-linearities. The work presented here applies the ideas motivated by non-linear dynamical systems theory—the Koopman Operator—to an innovative algorithm in the context of wind farm systems—Input Output Dynamic Mode Decomposition (IODMD)—to improve on the ability to model the aerodynamic interaction between wind turbines in a wind farm and uncover insights into the existing dynamics. It is shown that a reduced order linear state space model can reproduce the downstream turbine generator power dynamics and reconstruct the upstream turbine wake. It is further shown that the fit can be improved by judiciously choosing the Koopman observables used in the IODMD algorithm without jeopardizing the models ability to rebuild the turbine wake. The extensions to the IODMD algorithm provide an important step towards the design of linear reduced order models which can accurately reproduce the dynamics in a wind farm.